Vodka is not a very strongly flavored alcohol, so any sort of intense taste should cover the flavor up thoroughly. There are two sorts of drinks that will do the job quite well: sweet and tart, and salty and spicy. If you want to drink something salty and spicy, follow the link References to make a Bloody Mary.
Start with the vodka, and use as little as possible. The less vodka in the drink, the less you are going to taste it.
Mix up tart, sweet fruit juices. Both the tartness and the sweetness will help you cover the taste. For example, you can mix one part vodka with two parts each of orange juice and pineapple juice to make a bay breeze. Both juices are very sweet and tart, so they will help cover the flavor.
Consider adding simple syrup to the drink. Mixing in an ounce of simple syrup will make a sweet drink even sweeter, making it hard to taste the vodka.
Add a splash of lime or lemon juice. This will increase the tartness, further masking the taste of the vodka.
Add some soda water. The sensation of soda bubbles popping on your tongue will mask the subtle flavor of the vodka.
Add pieces of fruit to the drink. Fruit will soak up some of the alcohol. You will still feel the effect of the vodka when you drink it, but you won't taste it as much.
Add ice. Colder drinks go down more smoothly. Even if you still taste the vodka, it won't bother you as much.